No abstract

The procedure underlying the matching of 1-form (tetrad) fields in theories possessing absolute parallelism -f (T ) gravity being within this category-is addressed and exemplified. We show that the remnant symmetries of the intervening spaces play a central role in the process, because the knowledge of the remnant group of local Lorentz transformations enables one to perform rotations and/or boosts in order to C 1 -match the corresponding tetrads on the junction surface. This automatically ensures the continuity of the Weitzenböck scalar there, even though this proves to be just a necessary condition in order to obtain a global parallelization of the spacetime.

The automated search software integrated with a scanning electron microscope (SEM/EDS) has been the standard tool for detecting inorganic gunshot residues (iGSR) for several decades. The detection of these particles depends on various factors such as collection, preservation, contamination with organic matter, and the method for sample analysis. This article focuses on the influence of equipment resolution setup on the backscattered electron images of the sample. The pixel size of these images plays a crucial role in determining the detectability of iGSR particles, especially those with sizes close to the pixel size. In this study, we calculated the probability of missing all characteristic iGSR particles in a sample using an SEM/EDS automated search and how it depends on the image pixel resolution setup. We developed and validated an iGSR particle detection model that links particle size with equipment registers and applied it to 320 samples analyzed by a forensic science laboratory. Our results show that the probability of missing all characteristic iGSR particles due to their size is below 5% for pixel sizes below 0.32 μm2. These findings indicate that pixel sizes as large as twice the one commonly used in laboratory casework, that is, 0.16 μm2, are effective for initial sample scanning, yielding good detection rates of characteristic particles that could exponentially reduce laboratory workload.